Solve 8+2*10^-3*159.1549i/4*10^-3*159.1549i

$$\frac { 8 + 2 \times 10 ^ { - 3 } \times 159.1549 i } { 4 \times 10 ^ { - 3 } \times 159.1549 i }$$

Evaluate

$$0.5-\frac{20000000}{1591549}i\approx 0.5-12.566374017i$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{8+2\times \frac{1}{1000}\times \left(159.1549i\right)}{4\times 10^{-3}\times \left(159.1549i\right)}$$

Multiply 2 and \frac{1}{1000} to get \frac{1}{500}.

$$\frac{8+\frac{1}{500}\times \left(159.1549i\right)}{4\times 10^{-3}\times \left(159.1549i\right)}$$

Multiply \frac{1}{500} and 159.1549i to get \frac{1591549}{5000000}i.

$$\frac{8+\frac{1591549}{5000000}i}{4\times 10^{-3}\times \left(159.1549i\right)}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{8+\frac{1591549}{5000000}i}{4\times \frac{1}{1000}\times \left(159.1549i\right)}$$

Multiply 4 and \frac{1}{1000} to get \frac{1}{250}.

$$\frac{8+\frac{1591549}{5000000}i}{\frac{1}{250}\times \left(159.1549i\right)}$$

Multiply \frac{1}{250} and 159.1549i to get \frac{1591549}{2500000}i.

$$\frac{8+\frac{1591549}{5000000}i}{\frac{1591549}{2500000}i}$$

Multiply both numerator and denominator by imaginary unit i.

$$\frac{-\frac{1591549}{5000000}+8i}{-\frac{1591549}{2500000}}$$

Divide -\frac{1591549}{5000000}+8i by -\frac{1591549}{2500000} to get \frac{1}{2}-\frac{20000000}{1591549}i.

$$\frac{1}{2}-\frac{20000000}{1591549}i$$

Real Part

$$0.5$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$Re(\frac{8+2\times \frac{1}{1000}\times \left(159.1549i\right)}{4\times 10^{-3}\times \left(159.1549i\right)})$$

Multiply 2 and \frac{1}{1000} to get \frac{1}{500}.

$$Re(\frac{8+\frac{1}{500}\times \left(159.1549i\right)}{4\times 10^{-3}\times \left(159.1549i\right)})$$

Multiply \frac{1}{500} and 159.1549i to get \frac{1591549}{5000000}i.

$$Re(\frac{8+\frac{1591549}{5000000}i}{4\times 10^{-3}\times \left(159.1549i\right)})$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$Re(\frac{8+\frac{1591549}{5000000}i}{4\times \frac{1}{1000}\times \left(159.1549i\right)})$$

Multiply 4 and \frac{1}{1000} to get \frac{1}{250}.

$$Re(\frac{8+\frac{1591549}{5000000}i}{\frac{1}{250}\times \left(159.1549i\right)})$$

Multiply \frac{1}{250} and 159.1549i to get \frac{1591549}{2500000}i.

$$Re(\frac{8+\frac{1591549}{5000000}i}{\frac{1591549}{2500000}i})$$

Multiply both numerator and denominator of \frac{8+\frac{1591549}{5000000}i}{\frac{1591549}{2500000}i} by imaginary unit i.

$$Re(\frac{-\frac{1591549}{5000000}+8i}{-\frac{1591549}{2500000}})$$

Divide -\frac{1591549}{5000000}+8i by -\frac{1591549}{2500000} to get \frac{1}{2}-\frac{20000000}{1591549}i.

$$Re(\frac{1}{2}-\frac{20000000}{1591549}i)$$

The real part of \frac{1}{2}-\frac{20000000}{1591549}i is \frac{1}{2}.

$$\frac{1}{2}$$